The invention relates to a method and a device for calibrating parameters of sensor elements in a sensor array. The invention also relates to a computer program product for calibrating parameters of sensor elements of a sensor array when run on a programmable device and to a sensor array calibrated with a calibration method.
In sensor array systems, the, complex, receiver gains and sensor noise powers of the sensor elements in the sensor array are initially unknown and have to be calibrated. (Gain) calibration enhances the quality, specifically the sensitivity, of the sensor system and, moreover, improves the effectiveness of array signal processing techniques for interference mitigation.
Non-polarized and single polarization calibration techniques for sensor array systems are generally known in the art [1, 2, 3, 5, 13], and the statistical performance also is a well studied topic [1, 2, 3, 5, 8, 13, 14]. Recently, Hamaker, Bregman and Sault [10, 11, 12] developed, for radio astronomical purposes, a polarization formalism in which the polarization state of the received signal, and the propagation of these signals through the atmosphere and through the sensor array, were thoroughly and elegantly incorporated. This formalism is based on optics [15, 16] and on extensions of the (approximate) solutions in radio polarimetry [17, 18].
In this formalism, the polarized signal is described by a 2×2 size Stokes matrix [17, 18] (a Stokes matrix describes the polarization state of the signal: intensity, linearity, ellipticity, polarization angle, total polarization), and the distorting and propagation effects by a 2×2 size Jones matrix [10, 11, 12] which in general is different for each of the dual polarization array sensors. The output of a dual polarization channel is described by a multiplication of Jones and Stokes matrices. The polarized array formalism is further focussed on pair-wise correlation products involving 2×2 size Jones and Stokes matrices. However, solving systems based on this formalism require an iterative approach and convergence is not always guaranteed. Hence, in such systems stability is a problem as well.
The single polarization and non-polarized sensor array parameter estimation problem is well known from literature [2, 13]. However, these calibration methods are disadvantageous because they require a large amount of processing. They also require a good initial point (gain and noise values), which is not always available. Typically, the number of processing steps involved scales with the third power of the number of sensor elements.
Recently, fast and closed form single polarization calibration techniques were described in [1]. In this publication, the calibration techniques involves the comparison of an estimated signal with a signal outputted by telescopes in a telescope array. By optimisation of the estimated signal with a least square error minimalisation of the difference between the estimated and outputted signal, the gains of the telescopes can be derived. In the publication [1] several variants of the least square error minimalisation are described. One of the minimalisations is a logarithmic minimalisation, in which difference of the logarithms of the covariance of the estimated signals and the covariance of the outputted signals are compared.
The number of processing steps for the logarithmic minimalisation described in [1] scales with the square of the number of elements and is thus much much faster than conventional methods. However this logarithmic minimalisation has the disadvantage that, for unequal gains, the method is not efficient, which means that the estimation accuracy is lower than the theoretical bound.